https://file.aiquickdraw.com/mathbot/file/1730304545166j86ju17r.jpg

The problem asks to determine which rule explains why the two triangles are congruent. Let's analyze the information provided in the image:

1. Both triangles show markings on two sides, indicating that two pairs of sides are congruent.
2. There is also a marking on the angle between these two sides, indicating that the included angle is congruent.

Since we have two pairs of sides and the included angle in each triangle being congruent, this matches the **Side-Angle-Side (SAS)** congruence criterion. According to the SAS rule, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

**Correct answer:** **SAS**

Would you like a further breakdown of the SAS theorem or have any other questions?

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### Related Questions:
1. What are the criteria for the ASA (Angle-Side-Angle) congruence theorem?
2. Can triangles be proven congruent if only two angles are congruent?
3. How does the AAS (Angle-Angle-Side) theorem differ from the ASA theorem?
4. What is the importance of the "included angle" in the SAS theorem?
5. How do we use SSS (Side-Side-Side) to prove triangles are congruent?

**Tip:** Always identify the sides or angles marked in diagrams to quickly determine which congruence criterion applies.

Which rule explains why these triangles are congruent?

Explore how to use the Side-Angle-Side (SAS) congruence theorem to determine triangle congruence. This problem provides a visual representation of two triangles with two pairs of sides and an included angle marked, demonstrating the SAS criterion for congruence. Ideal for students in Grades 8-10 studying geometry.

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